We prove tight entropic uncertainty relations for a large number of mutuallyunbiased measurements. In particular, we show that a bound derived from theresult by Maassen and Uffink for 2 such measurements can in fact be tight forup to sqrt{d} measurements in mutually unbiased bases. We then show that usingmore mutually unbiased bases does not always lead to a better locking effect.We prove that the optimal bound for the accessible information using up tosqrt{d} specific mutually unbiased bases is log d/2, which is the same as canbe achieved by using only two bases. Our result indicates that merely usingmutually unbiased bases is not sufficient to achieve a strong locking effect,and we need to look for additional properties.
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机译：我们证明了大量无偏测量的紧密的熵不确定性关系。特别地，我们表明，由Maassen和Uffink从结果得出的关于2个这样的测量的界实际上可以在互不相同的基础上对于sqrt {d}测量是严格的。然后，我们证明使用更多互不偏基并不总是会导致更好的锁定效果。我们证明使用最多sqrt {d}个特定互不偏基的可访问信息的最佳界限是log d / 2，与canbe相同仅使用两个基准即可实现。我们的结果表明，仅使用相互无偏的碱基不足以实现强大的锁定效果，并且我们需要寻找其他属性。
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